比例加载路径下板料本构模型的建立及实验验证

根据单位体积塑性功相等原理，基于Druker公设以及等向强化模型，利用比例加载的特点，推导出板料在无卸载比例加载路径下的双向拉伸本构模型，并给出几种不同屈服准则下的本构模型。采用两种薄钢板BH220、SPEN进行了十字形双向拉伸实验研究，给出了这两种薄钢板在加载比例1：1和2：1情况下应力应变关系的理论曲线和实验曲线对比分析结果。结果表明，在小变形范围内，采用Hosford、Barlat89、Mises屈服准则得到的双向拉伸应力应变曲线与实验结果符合得较好。结合已有文献的研究结果说明：在小变形范围内以及无卸载比例加载路径下双向拉伸本构模型是正确性的；在小变形比例加载情况下，各向异性板料的强化规律为等向强化。     

高强钢板DP590温热环境下屈服准则适用性分析

板料成形过程中温度的变化会影响其塑性流动行为。以先进高强钢板DP590为研究对象,通过不同温度下单拉试验和不同温度不同加载比例双拉试验得到其在温热环境下的试验屈服轨迹,结果显示温度不仅会影响DP590钢板屈服轨迹的大小,而且影响屈服轨迹的形状。将试验屈服轨迹和几种理论屈服轨迹进行对比分析,表明Yld2000-2D屈服准则与试验结果吻合较好,同时等效应力应变点分析也显示出Yld2000-2D屈服准则满足塑性力学的单一曲线假设规律。针对Yld2000-2D屈服准则,采用不同温度下的试验数据计算出不同温度下的各向异性参数,通过拟合获得各向异性参数与温度的四次多项式函数关系,建立温度相关Yld2000-2D屈服准则,并与常规Yld2000-2D屈服准则对比分析,结果显示温度相关Yld2000-2D屈服准则更加适合描述DP590钢板温热环境下的屈服行为。     

不同强化模型下的板料成形极限

介绍Hill48屈服准则下基于不同强化模型的屈服方程。推导出能够用来确定随动强化模型和混合强化模型中参数的方程。采用单向拉伸曲线上所取得的数据,对所得方程进行拟合,得到参数值,并使用所得参数值得出三种强化模型下的单向拉伸曲线。结果表明采用上述方法能够准确地确定强化模型中的参数。给出随动强化模型和混合强化模型下成形极限的计算方法。基于三种强化模型,针对分散性失稳准则、Hill集中性失稳准则、凹槽失稳准则和平面应变漂移失稳准则,得到简单加载路径下的成形极限图和成形极限应力图。从这些图中可以看出,强化模型对成形极限图和成形极限应力图影响明显。因此应当确定板料在成形过程中的强化规律,选择合适的强化模型进行成形极限预测。     

各向异性非线性随动硬化本构模型的建立及应用

基于平面应力假设,采用HILL48各向异性屈服准则和A-F非线性随动硬化模型及塑性流动法则建立一种各向异性非线性随动硬化本构模型。运用向后欧拉回映算法,通过Fortran语言编写UMAT子程序,将该本构模型嵌入到ABAQUS软件中。以板料经过拉深筋的循环加载问题为研究对象,利用开发的本构模型、ABAQUS软件中的各向同性屈服及随动硬化模型对板料经过拉深筋的变形过程进行数值模拟分析,得到切向应力-应变循环变化曲线。对比试验结果,开发的弹塑性本构模型的计算精度更高,验证了所建本构模型的有效性,该模型可以应用于板料反向加载变形行为研究。     

40Cr调质钢高速冷滚打热力耦合数值模拟

在分析高速冷滚打成形原理的基础上,建立了热力耦合数学模型,通过常温和高温下不同应变速率的静态和动态压缩试验,结合Johnson-Cook流动应力公式,建立了40Cr调质钢的本构模型;利用有限元软件对40Cr调质钢高速冷滚打成形进行数值模拟,在考虑加工硬化与动态软化的综合效应下,获得了工件应力、应变和温度的分布,探讨了冷滚打成形过程中热力耦合形成的原因及成形速率对热效应的影响,并用试验进行了验证。结果表明:工件的温度分布和等效塑性应变分布是不均匀的,剧烈应变区的等效塑性应变高,温升高,难变形区的等效塑性应变低,温升低;试验结果证明了模拟分析的正确性。     

纯铁高温高应变率下的动态本构关系试验研究

利用带有加热装置和同步组装系统的分离式Hopkinson压杆装置对纯铁进行宽温度范围(293～1073K)、高应变速率(2000～8500s-1)下的动态力学性能测试试验,获得材料在不同温度和应变率耦合作用下的应力—应变曲线,从中探讨温度和应变率对纯铁塑性流动应力的影响机制。研究表明,纯铁具有明显的热软化效应、应变率强化效应和应变强化效应,流变应力随温度的降低和应变率的增加而提高;利用所测的应力—应变曲线拟合的Johnson-Cook本构模型可以较好地预测纯铁的塑性流变应力。     

CR1500HF热成形钢U形件不同位置的高速拉伸性能及其有限元模拟

在CR1500HF热成形钢U形件不同位置取样,进行应变速率在1～500 s-1的拉伸试验,研究了不同位置拉伸性能的差异和应变速率对热压成形件拉伸性能的影响;建立材料拉伸有限元模型,模拟分析了该钢的高速拉伸性能和拉伸试样加持端应力分布.结果表明:该热压成形U形件侧壁位置的抗拉强度和屈服强度低于法兰和底部位置,在进行碰撞分析时需考虑部分位置因冷却不足强度降低的影响;随着应变速率的增加,U形件不同位置的屈服强度和抗拉强度均增大;由拉伸有限元模型模拟得到的真应力-真塑性应变曲线与combined S-H本构模型拟合得到的曲线吻合较好,应变速率1,500 s-1下真应力均方根误差分别为19.98,39.48 MPa;高速拉伸过程中拉伸试样夹持端大部分处于弹性变形阶段,应变片粘贴位置距试样圆弧处的距离应大于19 mm.     

比例/非比例加载路径下5754O汽车用铝合金板各向异性变形行为的精确解析

随着越来越高的汽车轻量化需求,铝合金板在现代汽车工业中的应用越来越广。在不同加载路径下,包括比例和非比例加载,5754O铝合金板在塑性成形过程中具有复杂的各向异性规律。试验表明5754O铝合金板的各向异性规律随变形量的增加会发生改变,因此在常参数屈服准则理论框架下,基于传统的单一曲线假设难以对5754O铝合金板在整个塑性变形过程中的各向异性行为进行精确描述。鉴于上述问题,并同时考虑到大变形过程中材料变形的稳定性,对Yld2000-2d屈服准则进行改进。基于改进的Yld2000-2d屈服准则和单一曲线假设推导不同方向的单向拉伸应力应变曲线,并与试验结果进行了对比。结果表明,与原始的Yld2000-2d屈服准则不同,基于改进的Yld2000-2d屈服准则,传统的单一曲线假设仍然适用于5754O铝合金板各向异性问题。给出不同强化方式在比例加载路径下的统一性和非比例加载路径下的分散性证明。基于改进的Yld2000-2d屈服准则和等向强化和混合两种强化方式,推导非比例加载路径下板料的应力应变曲线。基于试验结果,验证了推导的理论曲线的精度。实现了5754O铝合金板在比例和非比例加载路径下变形行为的精确描述,为其工业应用提供了重要的理论支撑。     

金属板料冲压成形的数值模拟

本文采用有限元动力显式算法模拟金属板料冲压成形的加工过程。四结点蜕化壳单元和刚体壳单元分别用来建立权和模具的有限元模型;更新Ｌａｇｒａｎｇｅ法和速率型本构关系被用来处理板料变形中的大应变和大转动;材料模型采用塑性各向异性屈服与等向强化模型;通过主从面模型定义板料和模具的接触,接触算法采用运动约束法,摩擦力用库仓定律计算;并利用动力松弛法对回弹过程进行了计算。模拟结果和实际零件比较,证明模型合理,算法稳定,结果可靠,具有良好的应用价值。     

低频振动塑性成形粘弹塑性模型的体积效应分析

采用Kirchner对应变时间历程的基本假设,针对振动拉伸建立一个一维粘弹塑性模型;利用MATLAB中的符号计算,推导粘弹塑性本构方程的显式表达式.通过确立粘弹塑性边界并对本构方程进行数值求解,可以确定金属在振动加工过程中,其应力应变在粘弹性与粘塑性之间的变化情况.通过计算瞬时应变的大小与屈服限建立粘弹性变形和粘塑性变形的判断准则.在考虑粘弹塑性本构关系中的后继屈服情况、应变历程、应变率历程及弹性应变等因素后,可以确定单轴振动拉伸时材料变形的动态应力和平均应力.根据所给定的振型参数和材料力学性能参数,结合特定的振动拉伸实例,分别得出金属在准静态拉伸和振动拉伸时的动态应力-时间、动态应力-应变和平均应力-应变率的变化趋势等,实现基于粘弹塑性本构关系的低频振动塑性成形的体积效应机理分析.     

An experimental and theoretical analysis on the application of stress-based forming limit criterion

In this paper, a detailed study on the stress-based forming limit criterion (FLSD) during linear and complex strain paths is developed. The calculation of stress-based forming limits based on experimental strain data is performed by using the method proposed by Stoughton [A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 2000;42:1–27]. By applying several combinations of different constitutive equations on the required plastic calculation, an analysis on the experimental forming stress limits is performed. The necking phenomenon is simulated by Marciniack–Kuczinsky (M–K) model using a more general code for predicting the forming limits. The selected materials are a bake-hardened steel (BH steel) and an AA6016-T4 aluminium alloy. Several yield criteria such as Von Mises isotropic yield function, quadratic and non-quadratic criterion of Hill (A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society of London 1948;A193:281–97; Theoretical plasticity of textured aggregates. Mathematical Proceedings of the Cambridge Philosophical Society 1979;85:179–91) and the advanced Barlat Yld96 yield function are used to show the influence of the constitutive law incorporated in the analysis on the stress-based forming limits. The effect of the hardening model on the FLSD is analysed by using two hardening laws, namely Swift law and Voce law. The influence of work hardening coefficient, strain rate sensitivity and the balanced biaxial yield stress on the theoretical FLSD is also presented. The effect of strain path changes on the stress-based forming limits is analysed. Some relevant remarks about stress-based forming limit criterion concept are presented.     

耦合温度效应晶体塑性的TWIP钢变形行为研究

为探究TWIP钢高温条件下的塑性变形机理,建立了耦合温度效应的晶体塑性本构模型,考虑温度对TWIP钢滑移和孪生的影响,提出了耦合温度效应的流动法则和硬化法则。结合在500 ℃和750 ℃条件下的原位SEM高温拉伸试验,建立了描述TWIP钢热变形过程的晶体塑性有限元模型。模拟获得不同温度条件下的应力应变曲线、应变硬化率和孪晶体积分数与试验结果相吻合,验证了该模型的正确性。进而,基于所建立的模型研究了温度对TWIP钢塑性变形过程滑移、孪生演化及应变硬化过程的影响规律,结果表明：滑移阻力、孪生阻力和应变硬化率随温度的升高呈不均匀降低的趋势,且断后伸长率呈现降低的趋势,由25 ℃时53.4%降低至750 ℃时16.5%。同时,随温度升高,孪生受到抑制,但滑移受温度的影响较小,表现为滑移主导的塑性变形机制。     

Simulation and experimental verification of flexible roll forming of steel sheets

Roll forming is a sheet metal forming process that has been used for decades. Usually roll-formed sections have a constant cross section. Flexible roll forming is a brand new forming process that produces parts with variable cross sections, in which the rollers translate back and forth in a direction that is perpendicular to the sheet feeding direction. Theoretical analysis gives an explanation of the plane strain state, compressive stresses, tensile stresses, and shear stresses in flexible roll forming. In order to analyze the mechanics and the deformation characteristics of flexible roll forming, the finite element method (FEM) model of a 17-step flexible roll forming process is established. The yield criterion used in the FEM simulation is Hill 48, and the parameters of which are solved with the yield stresses under different loading conditions and are firstly verified with a plane strain tensile test. The complicated roller paths are realized with data extracted from the computer-aided design (CAD) files with VC++ programs developed by the authors. We developed the first flexible roll forming prototype machine in China, with which the roll forming experiment of a side door beam is performed. Final shapes of the experimental and numerical results are compared. It is shown that the numerical results based on Hill 48 yield criterion that is solved with yield stresses agree well with the experimental results, which indicates that the simulation model can well reflect the real forming process. Detailed analysis of the distribution and history of plastic strain, longitudinal strain, shear strain, and thickness of both the constant cross section and the variable cross section is performed, which is of great help to understand this forming process.     

A new yield function for compressible materials

A new yield function for compressible materials has been derived based upon a yield criterion postulated by the authors. This function was experimentally verified for the uniaxial state of compressive stress using the aluminum alloy X7091 as a model material, and excellent agreement was found between theoretical and experimental results for the density dependence of the yield and geometrical hardening. Yield surfaces for various density levels have been generated in a three-dimensional principal-stress space using computer graphics.     

Ideal stretch forming for minimum weight axisymmetric shell structures

A companion paper “Minimum Weight Design of Axisymmetric Shell Structures” by Richmond and Azarkhin describes the design of axisymmetric thin-walled structures and parts that can support specified loads with minimum material. The result is an optimum shape and thickness distribution in the final part when the strength of the material is assumed to be uniform. Here, we demonstrate the application of ideal forming theory to design sheet stretching processes that can produce the optimum shapes and thickness distributions from flat sheets of uniform thickness. Specific designs are achieved for producing minimum weight shell structures that will support a specified uniform pressure assuming both the Mises and the Tresca yield criteria along with the rigid-perfectly plastic flow condition. In the case of the Tresca yield condition, the optimum structure is a spherical shell segment with uniform thickness, and an associated ideal stretching process is hydraulic bulging. Because the effects of strain hardening have been neglected in the structural optimization theory, it has been possible here to design the minimum weight structure and its forming process sequentially. In subsequent work, we plan to include the effects of strain hardening on the shell strength, which will then require coupled design of the structure and its forming process. Also extension of these methods to three-dimensional geometries will be considered.     

Prediction of history-dependent forming limits by applying different hardening models

The loading history-dependent forming limits have been computed for sheet metals undergoing various combinations of plane-stress loading conditions. The analysis method is essentially an extension of Marciniak and Kucźynski's inhomogeneous model, except that the roles of isotropic and Prager-Ziegler kinematic hardening have been examined in detail while the flow theory of plasticity is applied. A suitable modification of the constitutive equations for the kinematic hardening model converts the rate form of the constitutive equations into the finite-increment form which satisfies the yield criterion precisely. Representative combinations of strain history consisted of an initial proportional straining to either a fixed strain state or different levels of strain state followed by continued loading under different conditions of strain ratios. Comparison of computed forming limits with available experimental data shows that the ultimate choice of either an isotropic or a kinematic hardening model is dependent on a specific combination of strain history and the material properties.     

高强铝合金热塑性变形本构关系研究现状及发展趋势

高强铝合金热成形工艺条件下的变形行为表征，需要在考虑温度、应变速率及应变影响的基础上结合微观演化行为建立热塑性本构关系。总结了高强铝合金热塑性变形本构关系相关研究成果。研究结果表明：广泛应用的唯象本构模型通过修正模型参数可以充分耦合应变、温度及应变速率作用，并准确地预测不同变形条件下的流动应力，然而缺乏对变形机制的明确解释，使得唯象本构模型对试验温度、应变速率变化范围较大以及试验条件范围外的变形行为预测精度难以得到保证；基于物理意义的本构模型能够模拟位错密度、晶粒尺寸及动态再结晶等微观演化过程，对流动应力进行精确计算，展现了强大的宏微观变形预测能力，是高强铝合金热塑性变形本构关系的研究趋势。     

A simulation of cold-roll forming for elastoplastic materials

A kinematical approach was proposed in a previous paper for predicting the optimal shape and the deformed length of a rigid-plastic metal sheet during cold-roll forming. Because the elastic effects are important in this kind of process, the method has been extended here to elastoplastic materials. In the new formulation, the sheet is still considered as a thin shell and its middle surface is described as a Coons patch depending on one geometrical parameter. Moreover, the material now satisfies a constitutive rate equation in which the corotational rate of stress is used. The Prandtl-Reuss model, including the von Mises yield criterion and the normality flow rule, is used. In order to integrate the elastoplastic constitutive equations, a radial return scheme is adapted so that the plastic power rate is calculated, using a Gauss method. Its minimization gives the optimal shape for a strain hardening elastoplastic material, as well as the optimal velocity field. This approach has been implemented on a workstation and, as for rigid-plastic materials, it gives a very fast simulation of the cold-roll forming process.